
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import tensorflow as tf
plt.rcParams['figure.figsize'] = [12, 6]
plt.rcParams.update({'font.size': 12})


df = pd.read_excel('columns.xlsx')
col = df['Symbol'].values
col = col.tolist()


df_stableFeedFlow = pd.read_csv(r'https://raw.githubusercontent.com/AshuPraja13/FCC-abnormality-detection/main/NOC_stableFeedFlow_outputs.csv',header=None)
df_stableFeedFlow.set_index = df_stableFeedFlow.iloc[:,0]
df_stableFeedFlow = df_stableFeedFlow.drop(columns=0)
df_stableFeedFlow.columns= col
df_stableFeedFlow.sample(5)


df_varyingFeedFlow=pd.read_csv(r'https://raw.githubusercontent.com/AshuPraja13/FCC-abnormality-detection/main/NOC_varyingFeedFlow_outputs.csv',header=None)
df_varyingFeedFlow.set_index = df_varyingFeedFlow.iloc[:,0]
df_varyingFeedFlow = df_varyingFeedFlow.drop(columns=0)
df_varyingFeedFlow.columns= col
df_varyingFeedFlow.sample(5)


df_condEff_decrease = pd.read_csv(r'https://raw.githubusercontent.com/AshuPraja13/FCC-abnormality-detection/main/condEff_decrease_outputs.csv',header=None)
df_condEff_decrease.set_index = df_condEff_decrease.iloc[:,0]
df_condEff_decrease = df_condEff_decrease.drop(columns=0)
df_condEff_decrease.columns= col
df_condEff_decrease.sample(5)


df_condEff_decrease.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1440 entries, 0 to 1439
Data columns (total 46 columns):
 #   Column       Non-Null Count  Dtype  
---  ------       --------------  -----  
 0   F3           1440 non-null   float64
 1   Tatm         1440 non-null   float64
 2   T1           1440 non-null   float64
 3   P4           1440 non-null   float64
 4   deltaP       1440 non-null   float64
 5   P6           1440 non-null   int64  
 6   Fair         1440 non-null   float64
 7   T3           1440 non-null   float64
 8   T2           1440 non-null   float64
 9   Tr           1440 non-null   float64
 10  Treg         1440 non-null   float64
 11  Lsp          1440 non-null   float64
 12  Tcyc         1440 non-null   float64
 13  Tcyc - Treg  1440 non-null   float64
 14  Cco,sg       1440 non-null   int64  
 15  Co2,sg       1440 non-null   float64
 16  P5           1440 non-null   float64
 17  V4           1440 non-null   float64
 18  V6           1440 non-null   float64
 19  V7           1440 non-null   float64
 20  V3           1440 non-null   float64
 21  V1           1440 non-null   float64
 22  V2           1440 non-null   float64
 23  Frgc         1440 non-null   int64  
 24  Fsc          1440 non-null   int64  
 25  ACAB         1440 non-null   float64
 26  AWGC         1440 non-null   float64
 27  F5           1440 non-null   float64
 28  F7           1440 non-null   float64
 29  Fsg          1440 non-null   float64
 30  FV11         1440 non-null   int64  
 31  P1           1440 non-null   float64
 32  P2           1440 non-null   float64
 33  FLPG         1440 non-null   float64
 34  FLN          1440 non-null   float64
 35  FHN          1440 non-null   float64
 36  FLCO         1440 non-null   float64
 37  FSlurry      1440 non-null   float64
 38  FReflux      1440 non-null   float64
 39  Tfra         1440 non-null   float64
 40  T10          1440 non-null   float64
 41  T20          1440 non-null   float64
 42  V9           1440 non-null   float64
 43  V8           1440 non-null   float64
 44  V10          1440 non-null   float64
 45  V11          1440 non-null   float64
dtypes: float64(41), int64(5)
memory usage: 517.6 KB


df_condEff_decrease.describe().T


sns.heatmap(df_condEff_decrease.corr(),cmap='coolwarm')

<AxesSubplot:>


for n,i in enumerate(df_stableFeedFlow.columns):
    plt.figure(figsize=(12,2))
    plt.plot(df_stableFeedFlow[i])
    plt.xlabel('time (mins)')
    plt.ylabel(i)
    plt.title(df[df['Symbol']==i]['Description'].values)
    plt.show()


for n,i in enumerate(df_varyingFeedFlow.columns):
    plt.figure(figsize=(12,2))
    plt.plot(df_varyingFeedFlow[i])
    plt.xlabel('time (mins)')
    plt.ylabel(i)
    plt.title(df[df['Symbol']==i]['Description'].values)
    plt.show()


for n,i in enumerate(df_condEff_decrease.columns):
    plt.figure(figsize=(12,2))
    plt.plot(df_condEff_decrease[i])
    plt.xlabel('time (mins)')
    plt.ylabel(i)
    plt.title(df[df['Symbol']==i]['Description'].values)
    plt.show()


from sklearn.preprocessing import StandardScaler
ss = StandardScaler()


X = ss.fit_transform(df_stableFeedFlow)


from sklearn.decomposition import PCA
pca = PCA()


X_pca = pca.fit_transform(X)


plt.figure(figsize=(15,6))
sns.set_style('whitegrid')
sns.lineplot(x=list(range(1,47)), y=np.cumsum(pca.explained_variance_ratio_), drawstyle='steps-pre')
sns.lineplot(x=list(range(0,46)),y=np.cumsum(pca.explained_variance_ratio_))
plt.xlabel('Eigen Values')
plt.ylabel('Ratio of Variance')
plt.title('Variance by each Eigen Value')
plt.show()


pca = PCA(n_components=10)
X_pca = pca.fit_transform(X)


plt.figure(figsize=(15,6))
sns.set_style('whitegrid')
sns.lineplot(x=list(range(1,11)), y=np.cumsum(pca.explained_variance_ratio_), drawstyle='steps-pre')
sns.lineplot(x=list(range(0,10)),y=np.cumsum(pca.explained_variance_ratio_))
plt.xlabel('Eigen Values')
plt.ylabel('Ratio of Variance')
plt.title('Variance by each Eigen Value')
plt.show()


X_train = X.reshape(2880,46,1)


# del model


model = tf.keras.models.Sequential()
model.add(tf.keras.layers.Bidirectional(tf.keras.layers.LSTM(256,return_sequences=True),input_shape=(46,1)))
model.add(tf.keras.layers.Dropout(0.2))
model.add(tf.keras.layers.Bidirectional(tf.keras.layers.LSTM(128,return_sequences=True)))
model.add(tf.keras.layers.Dropout(0.2))
model.add(tf.keras.layers.Dense(1))
model.compile(optimizer='adam', loss='mse', metrics=['mae'])
model.summary()

Model: "sequential"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 bidirectional (Bidirection  (None, 46, 512)           528384    
 al)                                                             
                                                                 
 dropout (Dropout)           (None, 46, 512)           0         
                                                                 
 bidirectional_1 (Bidirecti  (None, 46, 256)           656384    
 onal)                                                           
                                                                 
 dropout_1 (Dropout)         (None, 46, 256)           0         
                                                                 
 dense (Dense)               (None, 46, 1)             257       
                                                                 
=================================================================
Total params: 1185025 (4.52 MB)
Trainable params: 1185025 (4.52 MB)
Non-trainable params: 0 (0.00 Byte)
_________________________________________________________________


model.fit(X_train,X_train,epochs=30)

Epoch 1/30
90/90 [==============================] - 66s 406ms/step - loss: 0.1392 - mae: 0.1968
Epoch 2/30
90/90 [==============================] - 37s 407ms/step - loss: 0.0027 - mae: 0.0359
Epoch 3/30
90/90 [==============================] - 37s 407ms/step - loss: 0.0023 - mae: 0.0326
Epoch 4/30
90/90 [==============================] - 37s 414ms/step - loss: 0.0021 - mae: 0.0308
Epoch 5/30
90/90 [==============================] - 37s 410ms/step - loss: 0.0020 - mae: 0.0294
Epoch 6/30
90/90 [==============================] - 37s 409ms/step - loss: 0.0018 - mae: 0.0283
Epoch 7/30
90/90 [==============================] - 37s 413ms/step - loss: 0.0018 - mae: 0.0276
Epoch 8/30
90/90 [==============================] - 37s 413ms/step - loss: 0.0017 - mae: 0.0271
Epoch 9/30
90/90 [==============================] - 37s 415ms/step - loss: 0.0017 - mae: 0.0268
Epoch 10/30
90/90 [==============================] - 37s 414ms/step - loss: 0.0016 - mae: 0.0264
Epoch 11/30
90/90 [==============================] - 37s 414ms/step - loss: 0.0016 - mae: 0.0260
Epoch 12/30
90/90 [==============================] - 37s 416ms/step - loss: 0.0016 - mae: 0.0258
Epoch 13/30
90/90 [==============================] - 37s 414ms/step - loss: 0.0016 - mae: 0.0257
Epoch 14/30
90/90 [==============================] - 38s 418ms/step - loss: 0.0015 - mae: 0.0254
Epoch 15/30
90/90 [==============================] - 37s 413ms/step - loss: 0.0015 - mae: 0.0251
Epoch 16/30
90/90 [==============================] - 37s 412ms/step - loss: 0.0015 - mae: 0.0249
Epoch 17/30
90/90 [==============================] - 37s 413ms/step - loss: 0.0015 - mae: 0.0249
Epoch 18/30
90/90 [==============================] - 38s 420ms/step - loss: 0.0015 - mae: 0.0248
Epoch 19/30
90/90 [==============================] - 37s 415ms/step - loss: 0.0015 - mae: 0.0247
Epoch 20/30
90/90 [==============================] - 38s 419ms/step - loss: 0.0014 - mae: 0.0247
Epoch 21/30
90/90 [==============================] - 38s 420ms/step - loss: 0.0014 - mae: 0.0244
Epoch 22/30
90/90 [==============================] - 38s 425ms/step - loss: 0.0014 - mae: 0.0245
Epoch 23/30
90/90 [==============================] - 38s 418ms/step - loss: 0.0014 - mae: 0.0244
Epoch 24/30
90/90 [==============================] - 37s 411ms/step - loss: 0.0014 - mae: 0.0244
Epoch 25/30
90/90 [==============================] - 38s 428ms/step - loss: 0.0014 - mae: 0.0242
Epoch 26/30
90/90 [==============================] - 39s 438ms/step - loss: 0.0014 - mae: 0.0243
Epoch 27/30
90/90 [==============================] - 23s 253ms/step - loss: 0.0014 - mae: 0.0242
Epoch 28/30
90/90 [==============================] - 24s 266ms/step - loss: 0.0014 - mae: 0.0242
Epoch 29/30
90/90 [==============================] - 22s 247ms/step - loss: 0.0014 - mae: 0.0243
Epoch 30/30
90/90 [==============================] - 22s 249ms/step - loss: 0.0014 - mae: 0.0243

<keras.src.callbacks.History at 0x1c447022b50>


error_ae = []
for i in range(X.shape[0]):
    y_pred = model.predict(X[i].reshape(1,46,1),verbose=None)[0,:,0]
    error_ae.append(np.abs(X[i]-y_pred).sum())
AE_CL = np.percentile(error_ae,99)


pd.Series(error_ae).plot()
plt.hlines(AE_CL,0,len(error_ae),colors='red',linestyles='--')

<matplotlib.collections.LineCollection at 0x1c455024850>


X_reconstructed = np.dot(X_pca,pca.components_)
error_pca = X-X_reconstructed
Q_train = np.sum(np.abs(error_pca),axis=1)
Q_CL = np.percentile(Q_train,99)
# Q_train plot with CL
plt.figure()
plt.plot(Q_train, color='black')
plt.plot([1,len(Q_train)],[Q_CL,Q_CL], linestyle='--',color='red', linewidth=2)
plt.xlabel('Sample #')
plt.ylabel('Q metric: training data')
plt.title(f'Q metrix is max: {Q_train.max()} at:{Q_train.argmax()}mins')
plt.show()


lambda_ = np.diag(pca.explained_variance_)
lambda_inv = np.linalg.inv(lambda_)
T_train = np.zeros(X_pca.shape[0])
for i in range(X_pca.shape[0]):
    T_train[i] = np.dot(np.dot(X_pca[i],lambda_inv),X_pca[i].T)
T_CL = np.percentile(T_train,99)
# T2_train plot with CL
plt.figure()
plt.plot(T_train, color='black')
plt.plot([1,len(T_train)],[T_CL,T_CL], linestyle='--',color='red', linewidth=2)
plt.xlabel('Sample #')
plt.ylabel('T$^2$ metric: training data')
plt.title(f'T$^2$ metrix is max: {np.array(T_train).max()} at:{np.array(T_train).argmax()}mins')
plt.show()


cosine = []
ed = []
for i in range(X.shape[0]):
    v1 = X[i]
    v2 = np.dot(X_pca,pca.components_)[i]
    cosine.append(np.dot(v1,v2)/(np.linalg.norm(v1)*np.linalg.norm(v2)))
    ed.append(np.linalg.norm(v1 - v2))
C_CL = np.min(cosine)
E_CL = np.percentile(ed,99)
# pd.Series(ed).plot(color='black')
# plt.plot([1,len(ed)],[E_CL,E_CL], linestyle='--',color='red', linewidth=2)
# plt.show()
pd.Series(cosine).plot(color='black')
plt.plot([1,len(cosine)],[C_CL,C_CL], linestyle='--',color='red', linewidth=2)
plt.xlabel('Sample #')
plt.ylabel('Cosine similarity metric: training data')
plt.title(f'Cosine Similarity')
plt.show()


Q_CL,T_CL,C_CL,E_CL,AE_CL

(4.123113215519066,
 20.4243503525688,
 0.9427550112367161,
 0.9281694746755804,
 0.4919710296664876)


def Q_test(X,X_pca,pca_components_,Q_CL):
    X_reconstructed = np.dot(X_pca,pca_components_)
    error_pca = X-X_reconstructed
    Q_train = np.sum(np.abs(error_pca),axis=1)
    # Q_train plot with CL
    plt.figure()
    plt.plot(Q_train, color='black')
    plt.plot([1,len(Q_train)],[Q_CL,Q_CL], linestyle='--',color='red', linewidth=2)
    plt.xlabel('Sample #')
    plt.ylabel('Q metric: training data')
    plt.title(f'Q metrix is max: {Q_train.max()} at:{Q_train.argmax()}mins')
    plt.show()
    return error_pca


def T_test(X_pca,explained_variance_,TCL):
    lambda_ = np.diag(pca.explained_variance_)
    lambda_inv = np.linalg.inv(lambda_)
    T_train = np.zeros(X_pca.shape[0])
    for i in range(X_pca.shape[0]):
        T_train[i] = np.dot(np.dot(X_pca[i],lambda_inv),X_pca[i].T)
    # T2_train plot with CL
    plt.figure()
    plt.plot(T_train, color='black')
    plt.plot([1,len(T_train)],[T_CL,T_CL], linestyle='--',color='red', linewidth=2)
    plt.xlabel('Sample #')
    plt.ylabel('T$^2$ metric: training data')
    plt.title(f'T$^2$ metrix is max: {np.array(T_train).max()} at:{np.array(T_train).argmax()}mins')
    plt.show()


def cosine(X,X_transformed,pca_components_,C_CL,E_CL):
    cosine = []
    ed = []
    for i in range(X.shape[0]):
        v1 = X[i]
        v2 = np.dot(X_transformed,pca_components_)[i]
        cosine.append(np.dot(v1,v2)/(np.linalg.norm(v1)*np.linalg.norm(v2)))
        ed.append(np.linalg.norm(v1 - v2))
#     pd.Series(ed).plot(color='black')
#     plt.plot([1,len(ed)],[E_CL,E_CL], linestyle='--',color='red', linewidth=2)
#     plt.xlabel('Sample #')
#     plt.ylabel('Eucledian Distance metric: training data')
#     plt.show()
    pd.Series(cosine).plot(color='black')
    plt.plot([1,len(cosine)],[C_CL,C_CL], linestyle='--',color='red', linewidth=2)
    plt.xlabel('Sample #')
    plt.ylabel('Cosine similarity metric: training data')
    plt.title(f'Cosine Similarity')
    plt.show()


def autoencoder(df_test,CL):
    X_test = ss.transform(df_test)
    error_ae = []
    error_sum = []
    for i in range(X_test.shape[0]):
        y_pred = model.predict(X_test[i].reshape(1,46,1),verbose=None)[0,:,0]
        error_ae.append(np.abs(X_test[i]-y_pred))
        error_sum.append(np.abs(X_test[i]-y_pred).sum())
    error_ae=np.array(error_ae)
    pd.Series(error_sum).plot(color = 'black')
    plt.hlines(CL,0,len(error_ae),colors='red',linestyles='--')
    plt.xlabel('Sample #')
    plt.ylabel('Reconstruction error by Autoencoder')
    return error_ae


X = ss.transform(df_varyingFeedFlow)
X_test = pca.transform(X)


error_pca = Q_test(X,X_test,pca.components_,Q_CL)


T_test(X_test,pca.explained_variance_,T_CL)


cosine(X,X_test,pca.components_,C_CL,E_CL)


error_ae = autoencoder(df_varyingFeedFlow,AE_CL)


X = ss.transform(df_condEff_decrease)
X_test = pca.transform(X)


error_pca = Q_test(X,X_test,pca.components_,Q_CL)


T_test(X_test,pca.explained_variance_,T_CL)


cosine(X,X_test,pca.components_,C_CL,E_CL)


error_ae = autoencoder(df_condEff_decrease,AE_CL)


#%% Q contribution
error = np.abs(error_pca).sum(axis=1)
cum = []
for index,value in enumerate(error):
    if (value>Q_CL) and (len(cum)<15):
        previous_val = value
        cum.append(value)
        if len(cum) == 15:
            sample = index
            break
    else:
        cum=[]
# sample = ((pd.Series(error_pca.sum(axis=1))-pd.Series(error_pca.sum(axis=1)).shift()).abs()).argmax()
print('Time-',sample,'mins')
error_test_sample = error_pca[sample]
Q_contri = np.abs(error_test_sample) # *error_test_sample # vector of contributions

Time- 219 mins


plt.figure(figsize=[15,4])
plt.bar(['variable ' + str((i+1)) for i in range(len(Q_contri))], Q_contri)
plt.xticks(rotation = 80)
plt.ylabel('Q contributions')
plt.show()


plt.figure(figsize=(15,40))
print('Time-',sample,'mins')
for i,n in enumerate(np.argsort(Q_contri)[:-11:-1]):
    plt.subplot(5,2,i+1)
    plt.plot(df_condEff_decrease.iloc[:,n],'blue', linewidth=1)
    plt.xlabel('time (mins)')
    plt.ylabel(df['Symbol'][n])
    plt.title(df['Description'][n])
    plt.show

Time- 219 mins


#%% Autoencoder Error
error = np.abs(error_ae).sum(axis=1)
cum = []
for index,value in enumerate(error):
    if (value>AE_CL) and (len(cum)<15):
        previous_val = value
        cum.append(value)
        if len(cum) == 15:
            sample = index
            break
    else:
        cum=[]
# sample = ((pd.Series(error_ae.sum(axis=1))-pd.Series(error_ae.sum(axis=1)).shift()).abs()).argmax()
print('Time-',sample,'mins')
error_test_sample = error_pca[sample]
Q_contri = np.abs(error_test_sample) # *error_test_sample # vector of contributions

Time- 481 mins


plt.figure(figsize=(15,45))
print('Time-',sample,'mins')
for i,n in enumerate(np.argsort(error_ae[sample])[:-11:-1]):
    plt.subplot(5,2,i+1)
    plt.plot(df_condEff_decrease.iloc[:,n],'blue', linewidth=1)
    plt.xlabel('time (mins)')
    plt.ylabel(df['Symbol'][n])
    plt.title(df['Description'][n])
    plt.show

Time- 481 mins

	F3	Tatm	T1	P4	deltaP	P6	Fair	T3	T2	Tr	...	FLCO	FSlurry	FReflux	Tfra	T10	T20	V9	V8	V10	V11
632	164.85	79.961	460.98	34.4	-6.4	28	2.6806	1562.7	616.00	969.05	...	1644.7	212.78	2993.6	314.71	509.76	628.02	45.995	49.644	49.402	47.286
1759	165.28	78.490	460.25	34.4	-6.4	28	2.6872	1569.8	616.01	969.04	...	1647.0	209.61	3017.6	314.15	510.13	628.50	46.808	50.141	49.038	47.382
849	165.09	79.857	460.68	34.4	-6.4	28	2.6847	1566.0	616.02	969.06	...	1642.0	210.79	3006.4	314.88	509.92	628.18	45.873	49.829	48.649	47.118
2656	165.14	77.675	461.05	34.4	-6.4	28	2.6848	1564.0	615.99	969.04	...	1646.1	209.44	2987.6	313.13	509.96	628.23	48.028	49.813	48.804	47.349
1809	165.01	78.825	460.59	34.4	-6.4	28	2.6801	1566.1	616.01	968.99	...	1641.7	218.10	3003.6	314.25	509.93	628.41	46.728	49.886	49.767	47.099

	F3	Tatm	T1	P4	deltaP	P6	Fair	T3	T2	Tr	...	FLCO	FSlurry	FReflux	Tfra	T10	T20	V9	V8	V10	V11
3259	164.68	78.932	461.14	34.4	-6.4	28	2.6729	1560.6	616.00	968.96	...	1635.6	215.15	2915.0	312.66	509.18	627.24	48.220	48.679	49.227	46.820
3602	163.01	79.983	461.18	34.4	-6.4	28	2.6486	1550.1	616.00	969.00	...	1610.3	227.94	2732.3	310.08	507.40	624.66	50.636	46.035	48.098	45.560
361	166.80	78.746	461.15	34.4	-6.4	28	2.7136	1573.7	616.01	969.08	...	1675.9	197.06	3256.9	318.27	512.04	631.08	42.794	53.392	50.467	48.867
6655	164.37	79.734	461.51	34.4	-6.4	28	2.6710	1556.4	616.00	969.02	...	1629.5	211.65	2875.8	312.44	508.82	626.51	48.268	48.059	48.031	46.516
6216	162.63	79.331	460.62	34.4	-6.4	28	2.6415	1551.1	615.99	968.99	...	1603.4	226.02	2637.2	307.75	506.56	623.31	53.173	44.809	47.564	45.250

	F3	Tatm	T1	P4	deltaP	P6	Fair	T3	T2	Tr	...	FLCO	FSlurry	FReflux	Tfra	T10	T20	V9	V8	V10	V11
545	164.88	79.732	460.44	34.4	-6.4	28	2.6792	1566.1	616.00	969.01	...	1640.9	216.86	3044.1	317.97	509.83	628.21	42.217	49.937	49.582	47.062
1427	164.99	75.169	460.74	34.4	-6.4	28	2.6798	1565.0	616.00	969.00	...	1638.4	214.28	3025.6	317.74	509.68	627.93	42.521	49.668	49.428	46.934
1114	165.01	78.505	461.15	34.4	-6.4	28	2.6823	1562.6	615.99	969.02	...	1650.1	211.67	3094.6	320.84	509.93	628.25	39.116	50.300	50.083	47.580
340	164.59	78.586	460.67	34.4	-6.4	28	2.6733	1562.9	615.99	968.98	...	1640.6	223.55	2993.8	315.26	509.62	628.10	45.376	49.551	50.644	47.058
1051	165.03	78.948	460.82	34.4	-6.4	28	2.6820	1564.8	616.00	969.02	...	1641.1	212.26	3075.8	320.81	509.77	627.99	39.079	50.000	49.319	47.085

	count	mean	std	min	25%	50%	75%	max
F3	1440.0	164.964931	1.705031e-01	164.480000	164.840000	164.970000	165.080000	165.520000
Tatm	1440.0	78.342074	1.495206e+00	75.014000	77.206250	78.782000	79.699250	80.057000
T1	1440.0	460.921306	3.773500e-01	459.880000	460.660000	460.910000	461.190000	461.930000
P4	1440.0	34.400000	8.884870e-13	34.400000	34.400000	34.400000	34.400000	34.400000
deltaP	1440.0	-6.400001	1.366802e-05	-6.400300	-6.400000	-6.400000	-6.400000	-6.400000
P6	1440.0	28.000000	0.000000e+00	28.000000	28.000000	28.000000	28.000000	28.000000
Fair	1440.0	2.679885	3.071531e-03	2.671800	2.677700	2.680100	2.682000	2.689500
T3	1440.0	1563.718958	2.493819e+00	1557.700000	1561.900000	1563.500000	1565.200000	1571.900000
T2	1440.0	615.999910	6.663159e-03	615.980000	616.000000	616.000000	616.000000	616.020000
Tr	1440.0	968.999750	3.104291e-02	968.910000	968.980000	969.000000	969.020000	969.110000
Treg	1440.0	1250.001528	5.095774e-02	1249.900000	1250.000000	1250.000000	1250.000000	1250.100000
Lsp	1440.0	29.653098	9.399890e-02	29.376000	29.586000	29.655000	29.712000	29.905000
Tcyc	1440.0	1255.278958	5.024220e-02	1255.200000	1255.200000	1255.300000	1255.300000	1255.400000
Tcyc - Treg	1440.0	5.278488	3.785116e-02	5.186900	5.250175	5.280050	5.306625	5.388200
Cco,sg	1440.0	29881.611806	4.865322e+01	29737.000000	29846.000000	29880.000000	29917.250000	30009.000000
Co2,sg	1440.0	0.012470	1.691557e-04	0.012067	0.012344	0.012476	0.012599	0.012967
P5	1440.0	24.900000	6.752501e-13	24.900000	24.900000	24.900000	24.900000	24.900000
V4	1440.0	47.584573	1.025714e+00	45.364000	46.808000	47.828000	48.496000	48.969000
V6	1440.0	24.783957	1.008147e-01	24.532000	24.708000	24.797000	24.866250	25.033000
V7	1440.0	54.577801	6.263411e-02	54.413000	54.534000	54.582000	54.621000	54.773000
V3	1440.0	46.982188	1.595010e-02	46.937000	46.971000	46.982000	46.993000	47.025000
V1	1440.0	57.909178	1.800725e-01	57.470000	57.778500	57.893000	58.018500	58.493000
V2	1440.0	45.315724	5.301285e-02	45.177000	45.283000	45.317000	45.350000	45.481000
Frgc	1440.0	49572.265972	6.081201e+01	49407.000000	49529.000000	49576.000000	49614.000000	49765.000000
Fsc	1440.0	49572.208333	6.126321e+01	49411.000000	49529.000000	49577.000000	49614.000000	49764.000000
ACAB	1440.0	280.687479	1.405453e+00	277.550000	279.710000	281.055000	281.910000	282.860000
AWGC	1440.0	213.537201	6.912833e+00	198.490000	208.370000	215.240000	219.650000	222.610000
F5	1440.0	1989.637292	6.187052e+00	1974.600000	1985.175000	1989.100000	1993.400000	2009.700000
F7	1440.0	3735.766111	5.533026e+00	3722.500000	3731.800000	3735.800000	3739.800000	3752.000000
Fsg	1440.0	160.793049	1.845840e-01	160.310000	160.660000	160.810000	160.920000	161.370000
FV11	1440.0	29078.619444	7.483565e+02	27433.000000	28523.000000	29265.000000	29738.250000	30068.000000
P1	1440.0	14.637990	1.015644e-04	14.637000	14.638000	14.638000	14.638000	14.638000
P2	1440.0	35.044537	2.357305e-02	34.995000	35.026000	35.040000	35.063000	35.101000
FLPG	1440.0	3199.203681	1.250097e+02	2929.900000	3104.475000	3228.800000	3310.200000	3366.300000
FLN	1440.0	3751.406806	1.255117e+02	3582.700000	3640.875000	3721.100000	3844.300000	4029.600000
FHN	1440.0	711.221708	4.431817e+00	698.640000	708.587500	710.950000	713.720000	722.810000
FLCO	1440.0	1642.687292	4.569204e+00	1630.300000	1639.400000	1642.600000	1646.100000	1654.900000
FSlurry	1440.0	214.302257	4.559766e+00	201.700000	210.787500	214.325000	217.742500	225.080000
FReflux	1440.0	3038.856389	4.980395e+01	2923.500000	2999.575000	3050.200000	3077.500000	3127.300000
Tfra	1440.0	317.874403	3.343519e+00	310.700000	315.350000	318.700000	320.820000	322.170000
T10	1440.0	509.777910	1.371906e-01	509.380000	509.680000	509.770000	509.870000	510.130000
T20	1440.0	628.078812	1.482168e-01	627.680000	627.990000	628.080000	628.180000	628.400000
V9	1440.0	42.438248	3.860931e+00	37.629000	39.092250	41.394500	45.168750	51.247000
V8	1440.0	49.872215	3.110262e-01	49.160000	49.666000	49.880500	50.083500	50.627000
V10	1440.0	49.723878	6.232966e-01	47.978000	49.351750	49.678500	50.085000	51.357000
V11	1440.0	47.170649	2.520129e-01	46.496000	46.984000	47.164000	47.354250	47.844000

Decreased Main Column Overhead Condensor Efficiency¶

Introduction¶

Data Preprocessing¶

Exploratory Data Analysis (EDA)¶

Anomaly Detection Techniques¶

Data Cleaning, Feature Engineering, Predictive Modeling¶

Testing the model on Varying feed flow rate.¶

Testing the model on abnormal dataset.¶

Visualization¶

Conclusion¶

Future Work¶

*Decreased Main Column Overhead Condensor Efficiency*¶

Introduction¶

Data Preprocessing¶

Exploratory Data Analysis (EDA)¶

Anomaly Detection Techniques¶

Data Cleaning, Feature Engineering, Predictive Modeling¶

Testing the model on Varying feed flow rate.¶

Testing the model on abnormal dataset.¶

Visualization¶

Conclusion¶

Future Work¶

Decreased Main Column Overhead Condensor Efficiency¶